Question

The expected values, variances and standard Deviatiations for two random variables X and Y are given...

The expected values, variances and standard Deviatiations for two random variables X and Y are given in the following table

Variable expected value variance standard deviation
X 20 9 3
Y 35 25 5


Find the expected value and standard deviation of the following combinations of the variable X and Y. Round to nearest whole number.

E(X+10) =  ,

StDev(X+10) =

E(2X) =  ,

StDev(2X) =

E(3X-2) =  ,

StDev(3X-2) =

E(3X +4Y) =  ,

StDev(3X+4Y) =

E(X-2Y) =  ,

StDev(X-2Y) =

Homework Answers

Answer #1

E(X + 10) = E(X) + 10 = 20 + 10 = 30

SD(X + 10) = SD(X) + SD(10) = 3 + 0 = 3

E(2X) = 2 * E(X) = 2 * 20 = 40

SD(2X) = 2 * SD(X) = 2 * 3 = 6

E(3X - 2) = 3 * E(X) - 2 = 3 * 20 - 2 = 58

SD(3X - 2) = 3 * SD(X) - 0 = 3 * 3 = 9

E(3X + 4Y) = 3 * E(X) + 4 * E(Y) = 3 * 20 + 4 * 35 = 200

SD(3X + 4Y) = sqrt(Var(3X + 4Y)) = sqrt(32 * Var(X) + 42 * Var(Y)) = sqrt(9 * 9 + 16 * 25) = 22

E(X - 2Y) = E(X) - 2 * E(Y) = 20 - 2 * 35 = -50

SD(X - 2Y) = sqrt(Var(X - 2Y)) = sqrt(Var(X) + (-2)2 * Var(Y)) = sqrt(9 + 4 * 25) = 10

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Let X and Y be independent and normally distributed random variables with waiting values E (X)...
Let X and Y be independent and normally distributed random variables with waiting values E (X) = 3, E (Y) = 4 and variances V (X) = 2 and V (Y) = 3. a) Determine the expected value and variance for 2X-Y Waiting value µ = Variance σ2 = σ 2 = b) Determine the expected value and variance for ln (1 + X 2) c) Determine the expected value and variance for X / Y
Given independent random variables with means and standard deviations as​ shown, find the mean and standard...
Given independent random variables with means and standard deviations as​ shown, find the mean and standard deviation of each of these​ variables: Mean SD ​a) 4X                  ​b) 4Y+3 ​c) 2X+5Y X 70 14 ​d) 5X−4Y    ​e) X1+X2 Y 10 5 ​a) Find the mean and standard deviation for the random variable 4X. ​E(4​X)=_____________ ​SD(4​X)=_______________ ​(Round to two decimal places as​ needed.) ​b) Find the mean and standard deviation for the random variable 4​Y+3. ​E(4​Y+3​)= ________________ ​SD(4​Y+3​)= _____________________ ​(Round to...
Consider independent random variables X and Y , such that X has mean 2 and standard...
Consider independent random variables X and Y , such that X has mean 2 and standard deviation 4, and Y has mean 1 and standard deviation 9. Find the mean and standard deviation of the following random variables. a) 3X b) Y + 6 c) X + Y d) X − Y e) X1 + X2, where X1, X2 are independent copies of X.
If X, Y are random variables with E(X) = 2, Var(X) = 3, E(Y) = 1,...
If X, Y are random variables with E(X) = 2, Var(X) = 3, E(Y) = 1, Var(Y) =2, ρX,Y = −0.5 (a) For Z = 3X − 1 find µZ, σZ. (b) For T = 2X + Y find µT , σT (c) U = X^3 find approximate values of µU , σU
Let X and Y be jointly distributed random variables with means, E(X) = 1, E(Y) =...
Let X and Y be jointly distributed random variables with means, E(X) = 1, E(Y) = 0, variances, Var(X) = 4, Var(Y ) = 5, and covariance, Cov(X, Y ) = 2. Let U = 3X-Y +2 and W = 2X + Y . Obtain the following expectations: A.) Var(U): B.) Var(W): C. Cov(U,W): ans should be 29, 29, 21 but I need help showing how to solve.
Calculate the quantity of interest please. a) Let X,Y be jointly continuous random variables generated as...
Calculate the quantity of interest please. a) Let X,Y be jointly continuous random variables generated as follows: Select X = x as a uniform random variable on [0,1]. Then, select Y as a Gaussian random variable with mean x and variance 1. Compute E[Y ]. b) Let X,Y be jointly Gaussian, with mean E[X] = E[Y ] = 0, variances V ar[X] = 1,V ar[Y ] = 1 and covariance Cov[X,Y ] = 0.4. Compute E[(X + 2Y )2].
Suppose X and Y are continuous random variables with joint density function fX;Y (x; y) =...
Suppose X and Y are continuous random variables with joint density function fX;Y (x; y) = x + y on the square [0; 3] x [0; 3]. Compute E[X], E[Y], E[X2 + Y2], and Cov(3X - 4; 2Y +3).
Let X and Y be independent and identically distributed random variables with mean μ and variance...
Let X and Y be independent and identically distributed random variables with mean μ and variance σ2. Find the following: a) E[(X + 2)2] b) Var(3X + 4) c) E[(X - Y)2] d) Cov{(X + Y), (X - Y)}
Given below is a bivariate distribution for the random variables x and y. f(x, y) x...
Given below is a bivariate distribution for the random variables x and y. f(x, y) x y 0.1 90 90 0.5 30 40 0.4 50 70 a. Compute the expected value and the variance for x and y. E(x) = E(y) = Var(x) = Var(y) = b. Develop a probability distribution for x + y. Round your answers to one decimal place. x + y f(x + y) 180 70 120 c. Using the result of part (b), compute E(x...
15.1The probability density function of the X and Y compound random variables is given below. X                         &nbsp
15.1The probability density function of the X and Y compound random variables is given below. X                                        Y 1 2 3 1 234 225 84 2 180 453 161 3 39 192 157 Accordingly, after finding the possibilities for each value, the expected value, variance and standard deviation; Interpret the asymmetry measure (a3) when the 3rd moment (µ3 = 0.0005) according to the arithmetic mean and the kurtosis measure (a4) when the 4th moment (µ4 = 0.004) according to the arithmetic...
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT